Then, one has that \(R_{\lambda }=\pi (r_\lambda )\)  where the function \(r_\lambda \)  can be obtained from the Laplace transform of \(g_s\) . The use of the formula [1]} and a suitable change of variables provide
\(r_\lambda (x) := \frac{\Gamma \left(\frac{1}{2}-\lambda \right)}{{E}_B}\frac{\sqrt{2}\ell _B}{|x|} W_{\lambda ,0}\left(\frac{|x|^2}{2\ell _B^2}\right) \in L^1\big (\mathbb {R}^2\big )\cap L^2\big (\mathbb {R}^2\big ),\) 
